Physiological Mathematical Modeling

Due to exposure to micro-gravity, astronauts are at an elevated risk of developing renal (kidney) stones upon returning to normal gravitational levels. N&R Engineering has assisted NASA with probabilistic analyses of implemented deterministic models to determine the rate of calcium oxalate stone formation in the human kidney. A specialty deterministic code has been developed to simulate the physics of stone growth and passage through a single nephron (shown below). There are two types of nephrons that serve as the basic processing units of the kidney. These differ both in morphology and function. The average person has between 1-2 million nephrons of mixed type per kidney. The methodology developed has the capacity to include gravity, drag, and other relevant coupled physiochemical-hydrodynamic phenomena that affects the formation and growth of calcium oxalate stones. In particular, the concentration profiles of dissolved species, such as calcium and oxalate, as well as changes in velocity profile, may be specified along the length of a nephron to calculate stone growth under specified conditions.

The Probability Manager of PRODAF was used to perform probabilistic systems analyses on a set of representative nephrons to assess sensitivity to various system parameters. The system engineering and composite materials background of the N&R Engineering staff provided a versatile skillset that was able to approach the study of homeostatic control mechanisms such as those employed by the human body to regulate the activities of cells, tissues, and organs. Employing a diverse and flexible knowledge base, N&R has merged proven engineering techniques with cutting-edge quantitative biological modeling to solve medical problems relevant to the aerospace industry.

Services Provided:

Developed a general fault tree modeling framework for the renal system capable of accounting for changes in water intake over a limited range of 2.5L/day to 2.0L/day

Developed preliminary models to obtain a probability for growth of large CaOX crystals as an indicator of increased likelihood for producing renal stones.